Drivers look set for a nasty shock when they renew their car insurance this year, after premiums recorded their biggest ever increase during the last three months of last year.

According to the latest AA British Insurance Premium Index published today, the average insurance quote for those shopping around for a renewal rose by a wallet-busting 11% between September and December.

Overall, the average quoted comprehensive premium rose by 7.2%, sending it through the £1,000 a year barrier for the first time.

The quarterly index shows that the average "shoparound" premium – based on the three lowest quotes for a customer, which most closely resembles what buyers actually pay – accelerated steadily over the year, adding more than 22% to the typical comprehensive quote over the past 12 months. It ended the year at £613.

The cost of third party, fire and theft policies, typically bought by young and newly-qualified drivers, rose by a third over the year, sending it even further out of reach of many young motorists.

The AA's findings underline the importance of shopping around when you get your annual renewal notice. The disparity between the average quoted premium and the cheapest prices paid by those looking for the best deal has risen to £387 a year for comprehensive cover.

Simon Douglas, director of AA Insurance, said the increases were necessary because insurers had been paying out 20% more in claims than they had been collecting in premiums.

"Insurers have been reporting significant rises in personal injury claims. People now seem willing to pursue claims for minor injuries that in the past they wouldn't have bothered claiming for – all encouraged by personal injury claims lawyers," he said.

Douglas said the cost of meeting claims for accident damage had also been rising steadily, despite a fall in the number of accidents. "The spate of collisions during the recent wintry spells resulted in about 30% more claims than normal."

The AA's research shows the price rises are not evenly spread across the UK. The largest were in East Anglia, where motorists paid an average of 9.6% more in the last quarter of last year, while Wales saw the smallest increase at 5.7%.

Meanwhile, insurers have also seen fraud levels jump, adding £44 to every household's insurance cost. It is also estimated that uninsured drivers represent around one in 20 vehicles on Britain's roads, and claims involving such drivers added around £30 to every annual motor policy.

Adrian Webb, a spokesman for esure, said many consumers would be able to keep down the price they paid by looking around for better deals.

He added: "Unfortunately, there has been a surge in whiplash and small personal injury claims over recent years, despite there being less accidents.

"This inevitably pushes all insurers' premiums up and will affect drivers, while we battle to weed out spurious claimants and concentrate on paying only those who have genuinely suffered."

The AA warned that home insurance premiums were also on the rise. It said the average shoparound premium for combined buildings and contents cover rose by 9% last year.